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First, as to resistance generally. This is primarily of two
kinds ; in one part it is due to normal pressure caused by
the wind striking against the face of aflat surface (Fig. i),
in the other it is due to " skin friction " caused by the wind
rubbing against the sides of a plate that is moving edge on
(Fig. 2).
Dr. Stanton, of the National Physical Laboratory, also
various other authorities, have experimen ally established
an accepted formula for such normal pressure resistance in
the expression R as -003 V-, where R is in lbs. per square
foot of area facing the wind and V is in miles per hour.
In America, Dr. A. F. Zahm has experimentally pro
vided a formula that has not been generally accepted,
although one of the few that exist, in the expression
R = '0000316V1 •s°/0'93 (where R = resistance of double
surface per foot of span, / = chord of surface). This formula
may be approximated for aeroplane wings, within the ordinary
limits of modern flight speeds, by the simplified expression
R ~ • 000018V- (Fig. 3). And, as the expression itself is in
doubt, there is little object in being particular as to accuracy
in detail at the moment. In this expression, R represents
the resistance per unit of double surface moving as a plate
edge on to the wind. When the surfaces are separated, as
in the formation of a box or casing, where they would be
measured separately, the coefficient in the above formula
is halved to make it applicable to the single surface or external
area.
The important point to observe is that the relationship
between skin friction and normal pressure is represented by
the ratio of 1 to, approximately, 300. In other words, you
may use 300 square feet of edge on surface to enclose 1 square
foot of normal area, if you can ensure that this covering body
is truly edge on in effect.
Bodies of streamline form (Fig. 4), as understood in naval
architecture and in fluid dynamics generally, are supposed
to convert normal pressure into skin friction ; they, therefore,
JANUARY 6, 1912.
potentially are capable of reducing resistance witkin the
limits indicated by the above figures. This always assumes
of course, that Zahm's coefficient is approximately repre
sentative of the true state of affairs. If it is not, then the
substitution of a more accurate value will immediately show
the corresponding limits of possible gain.
In any case, these figures at least suggest the importance
of eliminating normal pressure from aeroplane design, by the
use of bodies of streamline form to enclose the larger masses
on the machine.
This body resistance—in which is included the resistance
of the struts, wires, and all framework except that actually
forming the wings—is a resistance that is proportionate to
the square of velocity (according to the above expression)
and is a kind of extra dead load on the machine. It bears no-
relationship to the lift of the wings, and is, consequently,
a detriment to efficiency. It is very important to dis
criminate thus between body resistance and the resistance
of the wings.
The resistance of an aeroplane wing in flight is itself of
two kinds, one being the above-discussed skin friction of the-
surfaces, while the other is a dynamic resistance due to the
creation of the aerial wave that supports the machine in flight.
This latter we may call the resistance due to load, and it
will be shown that it is a function of the effective angle of
the plane. If the effective angle is reduced, the resistance
due to load per unit of supporting area will be decreased,
but in order to support the same total load the area itself
must be increased, which in turn increases the resistance due
to skin friction.
Hence there is a relationship between the two kinds of
resistance experienced by a wing in flight, which is -why the
wing needs to be considered separately, and why it is not
proper to include the wing surface with the body surface
when calculating the skin friction resistance of the machine
as a whole.
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